// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `sender` to `recipient` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address sender, address recipient, uint256 amount) external returns (bool);

    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);
}

pragma solidity 0.7.6;


interface ISorbettoFragola {
    /// @notice The first of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token0() external view returns (address);

    /// @notice The second of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token1() external view returns (address);
    
    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);

    /// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform
    /// to the ERC20 specification
    /// @return The address of the Uniswap V3 Pool
    function pool() external view returns (IUniswapV3Pool);

    /// @notice The lower tick of the range
    function tickLower() external view returns (int24);

    /// @notice The upper tick of the range
    function tickUpper() external view returns (int24);

    /**
     * @notice Deposits tokens in proportion to the Sorbetto's current ticks.
     * @param amount0Desired Max amount of token0 to deposit
     * @param amount1Desired Max amount of token1 to deposit
     * @return shares minted
     * @return amount0 Amount of token0 deposited
     * @return amount1 Amount of token1 deposited
     */
    function deposit(uint256 amount0Desired, uint256 amount1Desired) external payable returns (uint256 shares, uint256 amount0,uint256 amount1);

    /**
     * @notice Withdraws tokens in proportion to the Sorbetto's holdings.
     * @dev Removes proportional amount of liquidity from Uniswap.
     * @param shares burned by sender
     * @return amount0 Amount of token0 sent to recipient
     * @return amount1 Amount of token1 sent to recipient
     */
    function withdraw(uint256 shares) external returns (uint256 amount0, uint256 amount1);

    /**
     * @notice Updates sorbetto's positions.
     * @dev Finds base position and limit position for imbalanced token
     * mints all amounts to this position(including earned fees)
     */
    function rerange() external;

    /**
     * @notice Updates sorbetto's positions. Can only be called by the governance.
     * @dev Swaps imbalanced token. Finds base position and limit position for imbalanced token if
     * we don't have balance during swap because of price impact.
     * mints all amounts to this position(including earned fees)
     */
    function rebalance() external;
}

pragma solidity 0.7.6;

interface ISorbettoStrategy {
    /// @notice Period of time that we observe for price slippage
    /// @return time in seconds
    function twapDuration() external view returns (uint32);

    /// @notice Maximum deviation of time waited avarage price in ticks
    function maxTwapDeviation() external view returns (int24);

    /// @notice Tick multuplier for base range calculation
    function tickRangeMultiplier() external view returns (int24);

    /// @notice The protocol's fee denominated in hundredths of a bip, i.e. 1e-6
    /// @return The fee
    function protocolFee() external view returns (uint24);

    /// @notice The price impact percentage during swap denominated in hundredths of a bip, i.e. 1e-6
    /// @return The max price impact percentage
    function priceImpactPercentage() external view returns (uint24);
}

pragma solidity >=0.5.0;

library PositionKey {
    /// @dev Returns the key of the position in the core library
    function compute(
        address owner,
        int24 tickLower,
        int24 tickUpper
    ) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(owner, tickLower, tickUpper));
    }
}

pragma solidity >=0.5.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
library TickMath {
    /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
    int24 internal constant MIN_TICK = -887272;
    /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
    int24 internal constant MAX_TICK = -MIN_TICK;

    /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
    uint160 internal constant MIN_SQRT_RATIO = 4295128739;
    /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
    uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
        uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
        require(absTick <= uint256(MAX_TICK), 'T');

        uint256 ratio = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
        if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
        if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
        if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
        if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
        if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
        if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
        if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
        if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
        if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
        if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
        if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
        if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
        if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
        if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
        if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
        if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
        if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
        if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
        if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;

        if (tick > 0) ratio = type(uint256).max / ratio;

        // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
        // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
        // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
        sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
    }

    /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
    /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
    /// ever return.
    /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96
    /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
    function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
        // second inequality must be < because the price can never reach the price at the max tick
        require(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO, 'R');
        uint256 ratio = uint256(sqrtPriceX96) << 32;

        uint256 r = ratio;
        uint256 msb = 0;

        assembly {
            let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(5, gt(r, 0xFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(4, gt(r, 0xFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(3, gt(r, 0xFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(2, gt(r, 0xF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(1, gt(r, 0x3))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := gt(r, 0x1)
            msb := or(msb, f)
        }

        if (msb >= 128) r = ratio >> (msb - 127);
        else r = ratio << (127 - msb);

        int256 log_2 = (int256(msb) - 128) << 64;

        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(63, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(62, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(61, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(60, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(59, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(58, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(57, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(56, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(55, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(54, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(53, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(52, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(51, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(50, f))
        }

        int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

        int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
        int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);

        tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
    }
}

pragma solidity >=0.5.0;



/// @title Liquidity amount functions
/// @notice Provides functions for computing liquidity amounts from token amounts and prices
library LiquidityAmounts {
    /// @notice Downcasts uint256 to uint128
    /// @param x The uint258 to be downcasted
    /// @return y The passed value, downcasted to uint128
    function toUint128(uint256 x) private pure returns (uint128 y) {
        require((y = uint128(x)) == x);
    }

    /// @notice Computes the amount of liquidity received for a given amount of token0 and price range
    /// @dev Calculates amount0 * (sqrt(upper) * sqrt(lower)) / (sqrt(upper) - sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount0 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount0(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        uint256 intermediate = FullMath.mulDiv(sqrtRatioAX96, sqrtRatioBX96, FixedPoint96.Q96);
        return toUint128(FullMath.mulDiv(amount0, intermediate, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the amount of liquidity received for a given amount of token1 and price range
    /// @dev Calculates amount1 / (sqrt(upper) - sqrt(lower)).
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount1 The amount1 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount1(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        return toUint128(FullMath.mulDiv(amount1, FixedPoint96.Q96, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the maximum amount of liquidity received for a given amount of token0, token1, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount of token0 being sent in
    /// @param amount1 The amount of token1 being sent in
    /// @return liquidity The maximum amount of liquidity received
    function getLiquidityForAmounts(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            liquidity = getLiquidityForAmount0(sqrtRatioAX96, sqrtRatioBX96, amount0);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            uint128 liquidity0 = getLiquidityForAmount0(sqrtRatioX96, sqrtRatioBX96, amount0);
            uint128 liquidity1 = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioX96, amount1);

            liquidity = liquidity0 < liquidity1 ? liquidity0 : liquidity1;
        } else {
            liquidity = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioBX96, amount1);
        }
    }

    /// @notice Computes the amount of token0 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    function getAmount0ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return
            FullMath.mulDiv(
                uint256(liquidity) << FixedPoint96.RESOLUTION,
                sqrtRatioBX96 - sqrtRatioAX96,
                sqrtRatioBX96
            ) / sqrtRatioAX96;
    }

    /// @notice Computes the amount of token1 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount1 The amount of token1
    function getAmount1ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
    }

    /// @notice Computes the token0 and token1 value for a given amount of liquidity, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    /// @return amount1 The amount of token1
    function getAmountsForLiquidity(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0, uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioX96, sqrtRatioBX96, liquidity);
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioX96, liquidity);
        } else {
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        }
    }
}

pragma solidity >=0.5.0;






/// @title Liquidity and ticks functions
/// @notice Provides functions for computing liquidity and ticks for token amounts and prices
library PoolVariables {
    using LowGasSafeMath for uint256;

    // Cache struct for calculations
    struct Info {
        uint256 amount0Desired;
        uint256 amount1Desired;
        uint256 amount0;
        uint256 amount1;
        uint128 liquidity;
        int24 tickLower;
        int24 tickUpper;
    }

    /// @dev Wrapper around `LiquidityAmounts.getAmountsForLiquidity()`.
    /// @param pool Uniswap V3 pool
    /// @param liquidity  The liquidity being valued
    /// @param _tickLower The lower tick of the range
    /// @param _tickUpper The upper tick of the range
    /// @return amounts of token0 and token1 that corresponds to liquidity
    function amountsForLiquidity(
        IUniswapV3Pool pool,
        uint128 liquidity,
        int24 _tickLower,
        int24 _tickUpper
    ) internal view returns (uint256, uint256) {
        //Get current price from the pool
        (uint160 sqrtRatioX96, , , , , , ) = pool.slot0();
        return
            LiquidityAmounts.getAmountsForLiquidity(
                sqrtRatioX96,
                TickMath.getSqrtRatioAtTick(_tickLower),
                TickMath.getSqrtRatioAtTick(_tickUpper),
                liquidity
            );
    }

    /// @dev Wrapper around `LiquidityAmounts.getLiquidityForAmounts()`.
    /// @param pool Uniswap V3 pool
    /// @param amount0 The amount of token0
    /// @param amount1 The amount of token1
    /// @param _tickLower The lower tick of the range
    /// @param _tickUpper The upper tick of the range
    /// @return The maximum amount of liquidity that can be held amount0 and amount1
    function liquidityForAmounts(
        IUniswapV3Pool pool,
        uint256 amount0,
        uint256 amount1,
        int24 _tickLower,
        int24 _tickUpper
    ) internal view returns (uint128) {
        //Get current price from the pool
        (uint160 sqrtRatioX96, , , , , , ) = pool.slot0();

        return
            LiquidityAmounts.getLiquidityForAmounts(
                sqrtRatioX96,
                TickMath.getSqrtRatioAtTick(_tickLower),
                TickMath.getSqrtRatioAtTick(_tickUpper),
                amount0,
                amount1
            );
    }

    /// @dev Amounts of token0 and token1 held in contract position.
    /// @param pool Uniswap V3 pool
    /// @param _tickLower The lower tick of the range
    /// @param _tickUpper The upper tick of the range
    /// @return amount0 The amount of token0 held in position
    /// @return amount1 The amount of token1 held in position
    function positionAmounts(IUniswapV3Pool pool, int24 _tickLower, int24 _tickUpper)
        internal
        view
        returns (uint256 amount0, uint256 amount1)
    {   
        //Compute position key
        bytes32 positionKey = PositionKey.compute(address(this), _tickLower, _tickUpper);
        //Get Position.Info for specified ticks
        (uint128 liquidity, , , uint128 tokensOwed0, uint128 tokensOwed1) =
            pool.positions(positionKey);
        // Calc amounts of token0 and token1 including fees
        (amount0, amount1) = amountsForLiquidity(pool, liquidity, _tickLower, _tickUpper);
        amount0 = amount0.add(uint256(tokensOwed0));
        amount1 = amount1.add(uint256(tokensOwed1));
    }

    /// @dev Amount of liquidity in contract position.
    /// @param pool Uniswap V3 pool
    /// @param _tickLower The lower tick of the range
    /// @param _tickUpper The upper tick of the range
    /// @return liquidity stored in position
    function positionLiquidity(IUniswapV3Pool pool, int24 _tickLower, int24 _tickUpper)
        internal
        view
        returns (uint128 liquidity)
    {
        //Compute position key
        bytes32 positionKey = PositionKey.compute(address(this), _tickLower, _tickUpper);
        //Get liquidity stored in position
        (liquidity, , , , ) = pool.positions(positionKey);
    }

    /// @dev Common checks for valid tick inputs.
    /// @param tickLower The lower tick of the range
    /// @param tickUpper The upper tick of the range
    function checkRange(int24 tickLower, int24 tickUpper) internal pure {
        require(tickLower < tickUpper, "TLU");
        require(tickLower >= TickMath.MIN_TICK, "TLM");
        require(tickUpper <= TickMath.MAX_TICK, "TUM");
    }

    /// @dev Rounds tick down towards negative infinity so that it's a multiple
    /// of `tickSpacing`.
    function floor(int24 tick, int24 tickSpacing) internal pure returns (int24) {
        int24 compressed = tick / tickSpacing;
        if (tick < 0 && tick % tickSpacing != 0) compressed--;
        return compressed * tickSpacing;
    }

    /// @dev Gets ticks with proportion equivalent to desired amount
    /// @param pool Uniswap V3 pool
    /// @param amount0Desired The desired amount of token0
    /// @param amount1Desired The desired amount of token1
    /// @param baseThreshold The range for upper and lower ticks
    /// @param tickSpacing The pool tick spacing
    /// @return tickLower The lower tick of the range
    /// @return tickUpper The upper tick of the range
    function getPositionTicks(IUniswapV3Pool pool, uint256 amount0Desired, uint256 amount1Desired, int24 baseThreshold, int24 tickSpacing) internal view returns(int24 tickLower, int24 tickUpper) {
        Info memory cache = 
            Info(amount0Desired, amount1Desired, 0, 0, 0, 0, 0);
        // Get current price and tick from the pool
        ( uint160 sqrtPriceX96, int24 currentTick, , , , , ) = pool.slot0();
        //Calc base ticks 
        (cache.tickLower, cache.tickUpper) = baseTicks(currentTick, baseThreshold, tickSpacing);
        //Calc amounts of token0 and token1 that can be stored in base range
        (cache.amount0, cache.amount1) = amountsForTicks(pool, cache.amount0Desired, cache.amount1Desired, cache.tickLower, cache.tickUpper);
        //Liquidity that can be stored in base range
        cache.liquidity = liquidityForAmounts(pool, cache.amount0, cache.amount1, cache.tickLower, cache.tickUpper);
        //Get imbalanced token
        bool zeroGreaterOne = amountsDirection(cache.amount0Desired, cache.amount1Desired, cache.amount0, cache.amount1);
        //Calc new tick(upper or lower) for imbalanced token
        if ( zeroGreaterOne) {
            uint160 nextSqrtPrice0 = SqrtPriceMath.getNextSqrtPriceFromAmount0RoundingUp(sqrtPriceX96, cache.liquidity, cache.amount0Desired, false);
            cache.tickUpper = PoolVariables.floor(TickMath.getTickAtSqrtRatio(nextSqrtPrice0), tickSpacing);
        }
        else{
            uint160 nextSqrtPrice1 = SqrtPriceMath.getNextSqrtPriceFromAmount1RoundingDown(sqrtPriceX96, cache.liquidity, cache.amount1Desired, false);
            cache.tickLower = PoolVariables.floor(TickMath.getTickAtSqrtRatio(nextSqrtPrice1), tickSpacing);
        }
        checkRange(cache.tickLower, cache.tickUpper);
        
        tickLower = cache.tickLower;
        tickUpper = cache.tickUpper;
    }

    /// @dev Gets amounts of token0 and token1 that can be stored in range of upper and lower ticks
    /// @param pool Uniswap V3 pool
    /// @param amount0Desired The desired amount of token0
    /// @param amount1Desired The desired amount of token1
    /// @param _tickLower The lower tick of the range
    /// @param _tickUpper The upper tick of the range
    /// @return amount0 amounts of token0 that can be stored in range
    /// @return amount1 amounts of token1 that can be stored in range
    function amountsForTicks(IUniswapV3Pool pool, uint256 amount0Desired, uint256 amount1Desired, int24 _tickLower, int24 _tickUpper) internal view returns(uint256 amount0, uint256 amount1) {
        uint128 liquidity = liquidityForAmounts(pool, amount0Desired, amount1Desired, _tickLower, _tickUpper);

        (amount0, amount1) = amountsForLiquidity(pool, liquidity, _tickLower, _tickUpper);
    }

    /// @dev Calc base ticks depending on base threshold and tickspacing
    function baseTicks(int24 currentTick, int24 baseThreshold, int24 tickSpacing) internal pure returns(int24 tickLower, int24 tickUpper) {
        
        int24 tickFloor = floor(currentTick, tickSpacing);

        tickLower = tickFloor - baseThreshold;
        tickUpper = tickFloor + baseThreshold;
    }

    /// @dev Get imbalanced token
    /// @param amount0Desired The desired amount of token0
    /// @param amount1Desired The desired amount of token1
    /// @param amount0 Amounts of token0 that can be stored in base range
    /// @param amount1 Amounts of token1 that can be stored in base range
    /// @return zeroGreaterOne true if token0 is imbalanced. False if token1 is imbalanced
    function amountsDirection(uint256 amount0Desired, uint256 amount1Desired, uint256 amount0, uint256 amount1) internal pure returns (bool zeroGreaterOne) {
        zeroGreaterOne =  amount0Desired.sub(amount0).mul(amount1Desired) > amount1Desired.sub(amount1).mul(amount0Desired) ?  true : false;
    }

    // Check price has not moved a lot recently. This mitigates price
    // manipulation during rebalance and also prevents placing orders
    // when it's too volatile.
    function checkDeviation(IUniswapV3Pool pool, int24 maxTwapDeviation, uint32 twapDuration) internal view {
        (, int24 currentTick, , , , , ) = pool.slot0();
        int24 twap = getTwap(pool, twapDuration);
        int24 deviation = currentTick > twap ? currentTick - twap : twap - currentTick;
        require(deviation <= maxTwapDeviation, "PSC");
    }

    /// @dev Fetches time-weighted average price in ticks from Uniswap pool for specified duration
    function getTwap(IUniswapV3Pool pool, uint32 twapDuration) internal view returns (int24) {
        uint32 _twapDuration = twapDuration;
        uint32[] memory secondsAgo = new uint32[](2);
        secondsAgo[0] = _twapDuration;
        secondsAgo[1] = 0;

        (int56[] memory tickCumulatives, ) = pool.observe(secondsAgo);
        return int24((tickCumulatives[1] - tickCumulatives[0]) / _twapDuration);
    }
}

pragma solidity >=0.5.0;

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface IUniswapV3PoolActions {

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @dev The caller of this method receives a callback in the form of IUniswapV3MintCallback#uniswapV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
    /// on tickLower, tickUpper, the amount of liquidity, and the current price.
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    /// @param data Any data that should be passed through to the callback
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Collects tokens owed to a position
    /// @dev Does not recompute fees earned, which must be done either via mint or burn of any amount of liquidity.
    /// Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
    /// amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
    /// actual tokens owed, e.g. type(uint128).max. Tokens owed may be from accumulated swap fees or burned liquidity.
    /// @param recipient The address which should receive the fees collected
    /// @param tickLower The lower tick of the position for which to collect fees
    /// @param tickUpper The upper tick of the position for which to collect fees
    /// @param amount0Requested How much token0 should be withdrawn from the fees owed
    /// @param amount1Requested How much token1 should be withdrawn from the fees owed
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);

    /// @notice Burn liquidity from the sender and account tokens owed for the liquidity to the position
    /// @dev Can be used to trigger a recalculation of fees owed to a position by calling with an amount of 0
    /// @dev Fees must be collected separately via a call to #collect
    /// @param tickLower The lower tick of the position for which to burn liquidity
    /// @param tickUpper The upper tick of the position for which to burn liquidity
    /// @param amount How much liquidity to burn
    /// @return amount0 The amount of token0 sent to the recipient
    /// @return amount1 The amount of token1 sent to the recipient
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// @dev The caller of this method receives a callback in the form of IUniswapV3SwapCallback#uniswapV3SwapCallback
    /// @param recipient The address to receive the output of the swap
    /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0
    /// @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
    /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
    /// value after the swap. If one for zero, the price cannot be greater than this value after the swap
    /// @param data Any data to be passed through to the callback
    /// @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
    /// @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);
}

pragma solidity >=0.5.0;

/// @title Pool state that is not stored
/// @notice Contains view functions to provide information about the pool that is computed rather than stored on the
/// blockchain. The functions here may have variable gas costs.
interface IUniswapV3PoolDerivedState {
    /// @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
    /// @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
    /// the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
    /// you must call it with secondsAgos = [3600, 0].
    /// @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
    /// log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
    /// @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
    /// @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
    /// @return secondsPerLiquidityCumulativeX128s Cumulative seconds per liquidity-in-range value as of each `secondsAgos` from the current block
    /// timestamp
    function observe(uint32[] calldata secondsAgos)
        external
        view
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);
}

pragma solidity >=0.5.0;

/// @title Pool state that can change
/// @notice These methods compose the pool's state, and can change with any frequency including multiple times
/// per transaction
interface IUniswapV3PoolState {
    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas
    /// when accessed externally.
    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value
    /// tick The current tick of the pool, i.e. according to the last tick transition that was run.
    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick
    /// boundary.
    /// observationIndex The index of the last oracle observation that was written,
    /// observationCardinality The current maximum number of observations stored in the pool,
    /// observationCardinalityNext The next maximum number of observations, to be updated when the observation.
    /// feeProtocol The protocol fee for both tokens of the pool.
    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0
    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0()
        external
        view
        returns (
            uint160 sqrtPriceX96,
            int24 tick,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext,
            uint8 feeProtocol,
            bool unlocked
        );

    /// @notice Returns the information about a position by the position's key
    /// @param key The position's key is a hash of a preimage composed by the owner, tickLower and tickUpper
    /// @return _liquidity The amount of liquidity in the position,
    /// Returns feeGrowthInside0LastX128 fee growth of token0 inside the tick range as of the last mint/burn/poke,
    /// Returns feeGrowthInside1LastX128 fee growth of token1 inside the tick range as of the last mint/burn/poke,
    /// Returns tokensOwed0 the computed amount of token0 owed to the position as of the last mint/burn/poke,
    /// Returns tokensOwed1 the computed amount of token1 owed to the position as of the last mint/burn/poke
    function positions(bytes32 key)
        external
        view
        returns (
            uint128 _liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        );
}

pragma solidity >=0.5.0;

/// @title Pool state that never changes
/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values
interface IUniswapV3PoolImmutables {

    /// @notice The first of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token0() external view returns (address);

    /// @notice The second of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token1() external view returns (address);

    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);
}

pragma solidity >=0.5.0;

/// @title The interface for a Uniswap V3 Pool
/// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform
/// to the ERC20 specification
/// @dev The pool interface is broken up into many smaller pieces
interface IUniswapV3Pool is
    IUniswapV3PoolImmutables,
    IUniswapV3PoolState,
    IUniswapV3PoolDerivedState,
    IUniswapV3PoolActions
{

}

pragma solidity 0.7.6;
pragma abicoder v2;



/// @title This library is created to conduct a variety of burn liquidity methods
library PoolActions {
    using PoolVariables for IUniswapV3Pool;
    using LowGasSafeMath for uint256;
    using SafeCast for uint256;

    /**
     * @notice Withdraws liquidity in share proportion to the Sorbetto's totalSupply.
     * @param pool Uniswap V3 pool
     * @param tickLower The lower tick of the range
     * @param tickUpper The upper tick of the range
     * @param totalSupply The amount of total shares in existence
     * @param share to burn
     * @param to Recipient of amounts
     * @return amount0 Amount of token0 withdrawed
     * @return amount1 Amount of token1 withdrawed
     */
    function burnLiquidityShare(
        IUniswapV3Pool pool,
        int24 tickLower,
        int24 tickUpper,
        uint256 totalSupply,
        uint256 share,
        address to
    ) internal returns (uint256 amount0, uint256 amount1) {
        require(totalSupply > 0, "TS");
        uint128 liquidityInPool = pool.positionLiquidity(tickLower, tickUpper);
        uint256 liquidity = uint256(liquidityInPool).mul(share) / totalSupply;
        

        if (liquidity > 0) {
            (amount0, amount1) = pool.burn(tickLower, tickUpper, liquidity.toUint128());

            if (amount0 > 0 || amount1 > 0) {
            // collect liquidity share
                (amount0, amount1) = pool.collect(
                    to,
                    tickLower,
                    tickUpper,
                    amount0.toUint128(),
                    amount1.toUint128()
                );
            }
        }
    }

    /**
     * @notice Withdraws exact amount of liquidity
     * @param pool Uniswap V3 pool
     * @param tickLower The lower tick of the range
     * @param tickUpper The upper tick of the range
     * @param liquidity to burn
     * @param to Recipient of amounts
     * @return amount0 Amount of token0 withdrawed
     * @return amount1 Amount of token1 withdrawed
     */
    function burnExactLiquidity(
        IUniswapV3Pool pool,
        int24 tickLower,
        int24 tickUpper,
        uint128 liquidity,
        address to
    ) internal returns (uint256 amount0, uint256 amount1) {
        uint128 liquidityInPool = pool.positionLiquidity(tickLower, tickUpper);
        require(liquidityInPool >= liquidity, "TML");
        (amount0, amount1) = pool.burn(tickLower, tickUpper, liquidity);

        if (amount0 > 0 || amount1 > 0) {
            // collect liquidity share including earned fees
            (amount0, amount0) = pool.collect(
                to,
                tickLower,
                tickUpper,
                amount0.toUint128(),
                amount1.toUint128()
            );
        }
    }

    /**
     * @notice Withdraws all liquidity in a range from Uniswap pool
     * @param pool Uniswap V3 pool
     * @param tickLower The lower tick of the range
     * @param tickUpper The upper tick of the range
     */
    function burnAllLiquidity(
        IUniswapV3Pool pool,
        int24 tickLower,
        int24 tickUpper
    ) internal {
        
        // Burn all liquidity in this range
        uint128 liquidity = pool.positionLiquidity(tickLower, tickUpper);
        if (liquidity > 0) {
            pool.burn(tickLower, tickUpper, liquidity);
        }
        
         // Collect all owed tokens
        pool.collect(
            address(this),
            tickLower,
            tickUpper,
            type(uint128).max,
            type(uint128).max
        );
    }
}

pragma solidity >=0.4.0;

// computes square roots using the babylonian method
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
library Babylonian {
    // credit for this implementation goes to
    // https://github.com/abdk-consulting/abdk-libraries-solidity/blob/master/ABDKMath64x64.sol#L687
    function sqrt(uint256 x) internal pure returns (uint256) {
        if (x == 0) return 0;
        // this block is equivalent to r = uint256(1) << (BitMath.mostSignificantBit(x) / 2);
        // however that code costs significantly more gas
        uint256 xx = x;
        uint256 r = 1;
        if (xx >= 0x100000000000000000000000000000000) {
            xx >>= 128;
            r <<= 64;
        }
        if (xx >= 0x10000000000000000) {
            xx >>= 64;
            r <<= 32;
        }
        if (xx >= 0x100000000) {
            xx >>= 32;
            r <<= 16;
        }
        if (xx >= 0x10000) {
            xx >>= 16;
            r <<= 8;
        }
        if (xx >= 0x100) {
            xx >>= 8;
            r <<= 4;
        }
        if (xx >= 0x10) {
            xx >>= 4;
            r <<= 2;
        }
        if (xx >= 0x8) {
            r <<= 1;
        }
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1; // Seven iterations should be enough
        uint256 r1 = x / r;
        return (r < r1 ? r : r1);
    }
}

pragma solidity ^0.7.0;


/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 * Since it is not possible to overflow a 256 bit integer with increments of one, `increment` can skip the {LowGasSafeMAth}
 * overflow check, thereby saving gas. This does assume however correct usage, in that the underlying `_value` is never
 * directly accessed.
 */
library Counters {
    using LowGasSafeMath for uint256;

    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        // The {LowGasSafeMath} overflow check can be skipped here, see the comment at the top
        counter._value += 1;
    }
}

pragma solidity >=0.7.0;

/// @title Function for getting the current chain ID
library ChainId {
    /// @dev Gets the current chain ID
    /// @return chainId The current chain ID
    function get() internal pure returns (uint256 chainId) {
        assembly {
            chainId := chainid()
        }
    }
}

pragma solidity =0.7.6;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (281): 0 < s < secp256k1n ÷ 2 + 1, and for v in (282): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        require(uint256(s) <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, "ISS");
        require(v == 27 || v == 28, "ISV");

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        require(signer != address(0), "IS");

        return signer;
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

pragma solidity =0.7.6;



/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;
    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = ChainId.get();
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (ChainId.get() == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(bytes32 typeHash, bytes32 name, bytes32 version) private view returns (bytes32) {
        return keccak256(
            abi.encode(
                typeHash,
                name,
                version,
                ChainId.get(),
                address(this)
            )
        );
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over `owner`'s tokens,
     * given `owner`'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for `permit`, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

pragma solidity >=0.6.0 <0.8.0;

/*
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with GSN meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

pragma solidity ^0.7.0;




/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin guidelines: functions revert instead
 * of returning `false` on failure. This behavior is nonetheless conventional
 * and does not conflict with the expectations of ERC20 applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20 {
    using LowGasSafeMath for uint256;

    mapping (address => uint256) private _balances;

    mapping (address => mapping (address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;
    uint8 private _decimals;

    /**
     * @dev Sets the values for {name} and {symbol}, initializes {decimals} with
     * a default value of 18.
     *
     * To select a different value for {decimals}, use {_setupDecimals}.
     *
     * All three of these values are immutable: they can only be set once during
     * construction.
     */
    constructor (string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
        _decimals = 18;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5,05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless {_setupDecimals} is
     * called.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return _decimals;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address sender, address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);
        _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "TEA"));
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].add(addedValue));
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].sub(subtractedValue, "DEB"));
        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(address sender, address recipient, uint256 amount) internal virtual {
        require(sender != address(0), "FZA");
        require(recipient != address(0), "TZA");

        _beforeTokenTransfer(sender, recipient, amount);

        _balances[sender] = _balances[sender].sub(amount, "TEB");
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(sender, recipient, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "MZA");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "BZA");

        _beforeTokenTransfer(account, address(0), amount);

        _balances[account] = _balances[account].sub(amount, "BEB");
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        require(owner != address(0), "AFZA");
        require(spender != address(0), "ATZA");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal virtual {
        _decimals = decimals_;
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be to transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual { }
}

pragma solidity =0.7.6;

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping (address => Counters.Counter) private _nonces;
 
    //keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    bytes32 private immutable _PERMIT_TYPEHASH = 0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) EIP712(name, "1") {
    }

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public virtual override {
        // solhint-disable-next-line not-rely-on-time
        require(block.timestamp <= deadline, "ED");

        bytes32 structHash = keccak256(
            abi.encode(
                _PERMIT_TYPEHASH,
                owner,
                spender,
                value,
                _useNonce(owner),
                deadline
            )
        );

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "IS");

        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view virtual override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    /**
     * @dev "Consume a nonce": return the current value and increment.
     */
    function _useNonce(address owner) internal virtual returns (uint256 current) {
        Counters.Counter storage nonce = _nonces[owner];
        current = nonce.current();
        nonce.increment();
    }
}

pragma solidity >=0.4.0;

/// @title FixedPoint96
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
/// @dev Used in SqrtPriceMath.sol
library FixedPoint96 {
    uint8 internal constant RESOLUTION = 96;
    uint256 internal constant Q96 = 0x1000000000000000000000000;
}

pragma solidity >=0.5.0;

/// @title Math functions that do not check inputs or outputs
/// @notice Contains methods that perform common math functions but do not do any overflow or underflow checks
library UnsafeMath {
    /// @notice Returns ceil(x / y)
    /// @dev division by 0 has unspecified behavior, and must be checked externally
    /// @param x The dividend
    /// @param y The divisor
    /// @return z The quotient, ceil(x / y)
    function divRoundingUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            z := add(div(x, y), gt(mod(x, y), 0))
        }
    }

    /// @notice Returns floor(x / y)
    /// @dev division by 0 has unspecified behavior, and must be checked externally
    /// @param x The dividend
    /// @param y The divisor
    /// @return z The quotient, floor(x / y)
    function unsafeDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            z := div(x, y)
        }
    }
}

pragma solidity >=0.4.0;

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 512-bit multiply [prod1 prod0] = a * b
        // Compute the product mod 2**256 and mod 2**256 - 1
        // then use the Chinese Remainder Theorem to reconstruct
        // the 512 bit result. The result is stored in two 256
        // variables such that product = prod1 * 2**256 + prod0
        uint256 prod0; // Least significant 256 bits of the product
        uint256 prod1; // Most significant 256 bits of the product
        assembly {
            let mm := mulmod(a, b, not(0))
            prod0 := mul(a, b)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        // Handle non-overflow cases, 256 by 256 division
        if (prod1 == 0) {
            require(denominator > 0);
            assembly {
                result := div(prod0, denominator)
            }
            return result;
        }

        // Make sure the result is less than 2**256.
        // Also prevents denominator == 0
        require(denominator > prod1);

        ///////////////////////////////////////////////
        // 512 by 256 division.
        ///////////////////////////////////////////////

        // Make division exact by subtracting the remainder from [prod1 prod0]
        // Compute remainder using mulmod
        uint256 remainder;
        assembly {
            remainder := mulmod(a, b, denominator)
        }
        // Subtract 256 bit number from 512 bit number
        assembly {
            prod1 := sub(prod1, gt(remainder, prod0))
            prod0 := sub(prod0, remainder)
        }

        // Factor powers of two out of denominator
        // Compute largest power of two divisor of denominator.
        // Always >= 1.
        uint256 twos = -denominator & denominator;
        // Divide denominator by power of two
        assembly {
            denominator := div(denominator, twos)
        }

        // Divide [prod1 prod0] by the factors of two
        assembly {
            prod0 := div(prod0, twos)
        }
        // Shift in bits from prod1 into prod0. For this we need
        // to flip `twos` such that it is 2**256 / twos.
        // If twos is zero, then it becomes one
        assembly {
            twos := add(div(sub(0, twos), twos), 1)
        }
        prod0 |= prod1 * twos;

        // Invert denominator mod 2**256
        // Now that denominator is an odd number, it has an inverse
        // modulo 2**256 such that denominator * inv = 1 mod 2**256.
        // Compute the inverse by starting with a seed that is correct
        // correct for four bits. That is, denominator * inv = 1 mod 2**4
        uint256 inv = (3 * denominator) ^ 2;
        // Now use Newton-Raphson iteration to improve the precision.
        // Thanks to Hensel's lifting lemma, this also works in modular
        // arithmetic, doubling the correct bits in each step.
        inv *= 2 - denominator * inv; // inverse mod 2**8
        inv *= 2 - denominator * inv; // inverse mod 2**16
        inv *= 2 - denominator * inv; // inverse mod 2**32
        inv *= 2 - denominator * inv; // inverse mod 2**64
        inv *= 2 - denominator * inv; // inverse mod 2**128
        inv *= 2 - denominator * inv; // inverse mod 2**256

        // Because the division is now exact we can divide by multiplying
        // with the modular inverse of denominator. This will give us the
        // correct result modulo 2**256. Since the precoditions guarantee
        // that the outcome is less than 2**256, this is the final result.
        // We don't need to compute the high bits of the result and prod1
        // is no longer required.
        result = prod0 * inv;
        return result;
    }

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        result = mulDiv(a, b, denominator);
        if (mulmod(a, b, denominator) > 0) {
            require(result < type(uint256).max);
            result++;
        }
    }
}

pragma solidity >=0.5.0;

/// @title Safe casting methods
/// @notice Contains methods for safely casting between types
library SafeCast {
    /// @notice Cast a uint256 to a uint160, revert on overflow
    /// @param y The uint256 to be downcasted
    /// @return z The downcasted integer, now type uint160
    function toUint160(uint256 y) internal pure returns (uint160 z) {
        require((z = uint160(y)) == y);
    }

    /// @notice Cast a uint256 to a uint128, revert on overflow
    /// @param y The uint256 to be downcasted
    /// @return z The downcasted integer, now type uint128
    function toUint128(uint256 y) internal pure returns (uint128 z) {
        require((z = uint128(y)) == y);
    }

    /// @notice Cast a int256 to a int128, revert on overflow or underflow
    /// @param y The int256 to be downcasted
    /// @return z The downcasted integer, now type int128
    function toInt128(int256 y) internal pure returns (int128 z) {
        require((z = int128(y)) == y);
    }

    /// @notice Cast a uint256 to a int256, revert on overflow
    /// @param y The uint256 to be casted
    /// @return z The casted integer, now type int256
    function toInt256(uint256 y) internal pure returns (int256 z) {
        require(y < 2**255);
        z = int256(y);
    }
}

pragma solidity >=0.7.0;

/// @title Optimized overflow and underflow safe math operations
/// @notice Contains methods for doing math operations that revert on overflow or underflow for minimal gas cost
library LowGasSafeMath {
    /// @notice Returns x + y, reverts if sum overflows uint256
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x);
    }

    /// @notice Returns x - y, reverts if underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x - y) <= x);
    }

    /// @notice Returns x * y, reverts if overflows
    /// @param x The multiplicand
    /// @param y The multiplier
    /// @return z The product of x and y
    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(x == 0 || (z = x * y) / x == y);
    }

    /// @notice Returns x - y, reverts if underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub(uint256 x, uint256 y, string memory errorMessage) internal pure returns (uint256 z) {
        require((z = x - y) <= x, errorMessage);
    }

    /// @notice Returns x + y, reverts if overflows or underflows
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add(int256 x, int256 y) internal pure returns (int256 z) {
        require((z = x + y) >= x == (y >= 0));
    }

    /// @notice Returns x - y, reverts if overflows or underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub(int256 x, int256 y) internal pure returns (int256 z) {
        require((z = x - y) <= x == (y >= 0));
    }

    /// @notice Returns x + y, reverts if sum overflows uint128
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add128(uint128 x, uint128 y) internal pure returns (uint128 z) {
        require((z = x + y) >= x);
    }

    /// @notice Returns x - y, reverts if underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub128(uint128 x, uint128 y) internal pure returns (uint128 z) {
        require((z = x - y) <= x);
    }

    /// @notice Returns x * y, reverts if overflows
    /// @param x The multiplicand
    /// @param y The multiplier
    /// @return z The product of x and y
    function mul128(uint128 x, uint128 y) internal pure returns (uint128 z) {
        require(x == 0 || (z = x * y) / x == y);
    }

    /// @notice Returns x + y, reverts if sum overflows uint128
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add160(uint160 x, uint160 y) internal pure returns (uint160 z) {
        require((z = x + y) >= x);
    }

    /// @notice Returns x - y, reverts if underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub160(uint160 x, uint160 y) internal pure returns (uint160 z) {
        require((z = x - y) <= x);
    }

    /// @notice Returns x * y, reverts if overflows
    /// @param x The multiplicand
    /// @param y The multiplier
    /// @return z The product of x and y
    function mul160(uint160 x, uint160 y) internal pure returns (uint160 z) {
        require(x == 0 || (z = x * y) / x == y);
    }
}

pragma solidity >=0.5.0;






/// @title Functions based on Q64.96 sqrt price and liquidity
/// @notice Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas
library SqrtPriceMath {
    using LowGasSafeMath for uint256;
    using SafeCast for uint256;

    /// @notice Gets the next sqrt price given a delta of token0
    /// @dev Always rounds up, because in the exact output case (increasing price) we need to move the price at least
    /// far enough to get the desired output amount, and in the exact input case (decreasing price) we need to move the
    /// price less in order to not send too much output.
    /// The most precise formula for this is liquidity * sqrtPX96 / (liquidity +- amount * sqrtPX96),
    /// if this is impossible because of overflow, we calculate liquidity / (liquidity / sqrtPX96 +- amount).
    /// @param sqrtPX96 The starting price, i.e. before accounting for the token0 delta
    /// @param liquidity The amount of usable liquidity
    /// @param amount How much of token0 to add or remove from virtual reserves
    /// @param add Whether to add or remove the amount of token0
    /// @return The price after adding or removing amount, depending on add
    function getNextSqrtPriceFromAmount0RoundingUp(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amount,
        bool add
    ) internal pure returns (uint160) {
        // we short circuit amount == 0 because the result is otherwise not guaranteed to equal the input price
        if (amount == 0) return sqrtPX96;
        uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;

        if (add) {
            uint256 product;
            if ((product = amount * sqrtPX96) / amount == sqrtPX96) {
                uint256 denominator = numerator1 + product;
                if (denominator >= numerator1)
                    // always fits in 160 bits
                    return uint160(FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator));
            }

            return uint160(UnsafeMath.divRoundingUp(numerator1, (numerator1 / sqrtPX96).add(amount)));
        } else {
            uint256 product;
            // if the product overflows, we know the denominator underflows
            // in addition, we must check that the denominator does not underflow
            require((product = amount * sqrtPX96) / amount == sqrtPX96 && numerator1 > product);
            uint256 denominator = numerator1 - product;
            return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
        }
    }

    /// @notice Gets the next sqrt price given a delta of token1
    /// @dev Always rounds down, because in the exact output case (decreasing price) we need to move the price at least
    /// far enough to get the desired output amount, and in the exact input case (increasing price) we need to move the
    /// price less in order to not send too much output.
    /// The formula we compute is within <1 wei of the lossless version: sqrtPX96 +- amount / liquidity
    /// @param sqrtPX96 The starting price, i.e., before accounting for the token1 delta
    /// @param liquidity The amount of usable liquidity
    /// @param amount How much of token1 to add, or remove, from virtual reserves
    /// @param add Whether to add, or remove, the amount of token1
    /// @return The price after adding or removing `amount`
    function getNextSqrtPriceFromAmount1RoundingDown(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amount,
        bool add
    ) internal pure returns (uint160) {
        // if we're adding (subtracting), rounding down requires rounding the quotient down (up)
        // in both cases, avoid a mulDiv for most inputs
        if (add) {
            uint256 quotient =
                (
                    amount <= type(uint160).max
                        ? (amount << FixedPoint96.RESOLUTION) / liquidity
                        : FullMath.mulDiv(amount, FixedPoint96.Q96, liquidity)
                );

            return uint256(sqrtPX96).add(quotient).toUint160();
        } else {
            uint256 quotient =
                (
                    amount <= type(uint160).max
                        ? UnsafeMath.divRoundingUp(amount << FixedPoint96.RESOLUTION, liquidity)
                        : FullMath.mulDivRoundingUp(amount, FixedPoint96.Q96, liquidity)
                );

            require(sqrtPX96 > quotient);
            // always fits 160 bits
            return uint160(sqrtPX96 - quotient);
        }
    }
}

pragma solidity >=0.6.0;


library TransferHelper {
    /// @notice Transfers tokens from the targeted address to the given destination
    /// @notice Errors with 'STF' if transfer fails
    /// @param token The contract address of the token to be transferred
    /// @param from The originating address from which the tokens will be transferred
    /// @param to The destination address of the transfer
    /// @param value The amount to be transferred
    function safeTransferFrom(
        address token,
        address from,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) =
            token.call(abi.encodeWithSelector(IERC20.transferFrom.selector, from, to, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'STF');
    }

    /// @notice Transfers tokens from msg.sender to a recipient
    /// @dev Errors with ST if transfer fails
    /// @param token The contract address of the token which will be transferred
    /// @param to The recipient of the transfer
    /// @param value The value of the transfer
    function safeTransfer(
        address token,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.transfer.selector, to, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'ST');
    }

    /// @notice Transfers ETH to the recipient address
    /// @dev Fails with `STE`
    /// @param to The destination of the transfer
    /// @param value The value to be transferred
    function safeTransferETH(address to, uint256 value) internal {
        (bool success, ) = to.call{value: value}(new bytes(0));
        require(success, 'STE');
    }
}


pragma solidity ^0.7.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor () {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "RC");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;

        _;

        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
}

pragma solidity =0.7.6;


/// @title Interface for WETH9
interface IWETH9 is IERC20 {
    /// @notice Deposit ether to get wrapped ether
    function deposit() external payable;
}

pragma solidity 0.7.6;

/// @title Sorbetto Fragola is a yield enchancement v3 contract
/// @dev Sorbetto fragola is a Uniswap V3 yield enchancement contract which acts as
/// intermediary between the user who wants to provide liquidity to specific pools
/// and earn fees from such actions. The contract ensures that user position is in 
/// range and earns maximum amount of fees available at current liquidity utilization
/// rate. 
contract SorbettoFragola is ERC20Permit, ReentrancyGuard, ISorbettoFragola {
    using LowGasSafeMath for uint256;
    using LowGasSafeMath for uint160;
    using LowGasSafeMath for uint128;
    using UnsafeMath for uint256;
    using SafeCast for uint256;
    using PoolVariables for IUniswapV3Pool;
    using PoolActions for IUniswapV3Pool;
    
    //Any data passed through by the caller via the IUniswapV3PoolActions#mint call
    struct MintCallbackData {
        address payer;
    }
    //Any data passed through by the caller via the IUniswapV3PoolActions#swap call
    struct SwapCallbackData {
        bool zeroForOne;
    }
    // Info of each user
    struct UserInfo {
        uint256 token0Rewards; // The amount of fees in token 0
        uint256 token1Rewards; // The amount of fees in token 1
        uint256 token0PerSharePaid; // Token 0 reward debt 
        uint256 token1PerSharePaid; // Token 1 reward debt
    }

    /// @notice Emitted when user adds liquidity
    /// @param sender The address that minted the liquidity
    /// @param liquidity The amount of liquidity added by the user to position
    /// @param amount0 How much token0 was required for the added liquidity
    /// @param amount1 How much token1 was required for the added liquidity
    event Deposit(
        address indexed sender,
        uint256 liquidity,
        uint256 amount0,
        uint256 amount1
    );
    
    /// @notice Emitted when user withdraws liquidity
    /// @param sender The address that minted the liquidity
    /// @param shares of liquidity withdrawn by the user from the position
    /// @param amount0 How much token0 was required for the added liquidity
    /// @param amount1 How much token1 was required for the added liquidity
    event Withdraw(
        address indexed sender,
        uint256 shares,
        uint256 amount0,
        uint256 amount1
    );
    
    /// @notice Emitted when fees was collected from the pool
    /// @param feesFromPool0 Total amount of fees collected in terms of token 0
    /// @param feesFromPool1 Total amount of fees collected in terms of token 1
    /// @param usersFees0 Total amount of fees collected by users in terms of token 0
    /// @param usersFees1 Total amount of fees collected by users in terms of token 1
    event CollectFees(
        uint256 feesFromPool0,
        uint256 feesFromPool1,
        uint256 usersFees0,
        uint256 usersFees1
    );

    /// @notice Emitted when sorbetto fragola changes the position in the pool
    /// @param tickLower Lower price tick of the positon
    /// @param tickUpper Upper price tick of the position
    /// @param amount0 Amount of token 0 deposited to the position
    /// @param amount1 Amount of token 1 deposited to the position
    event Rerange(
        int24 tickLower,
        int24 tickUpper,
        uint256 amount0,
        uint256 amount1
    );
    
    /// @notice Emitted when user collects his fee share
    /// @param sender User address
    /// @param fees0 Exact amount of fees claimed by the users in terms of token 0 
    /// @param fees1 Exact amount of fees claimed by the users in terms of token 1
    event RewardPaid(
        address indexed sender,
        uint256 fees0,
        uint256 fees1
    );
    
    /// @notice Shows current Sorbetto's balances
    /// @param totalAmount0 Current token0 Sorbetto's balance
    /// @param totalAmount1 Current token1 Sorbetto's balance
    event Snapshot(uint256 totalAmount0, uint256 totalAmount1);

    event TransferGovernance(address indexed previousGovernance, address indexed newGovernance);
    
    /// @notice Prevents calls from users
    modifier onlyGovernance {
        require(msg.sender == governance, "OG");
        _;
    }
    
    mapping(address => UserInfo) public userInfo; // Info of each user that provides liquidity tokens.
    /// @inheritdoc ISorbettoFragola
    address public immutable override token0;
    /// @inheritdoc ISorbettoFragola
    address public immutable override token1;
    // WETH address
    address public immutable weth = 0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2;
    // @inheritdoc ISorbettoFragola
    int24 public immutable override tickSpacing;
    uint24 immutable GLOBAL_DIVISIONER = 1e6; // for basis point (0.0001%)

    // @inheritdoc ISorbettoFragola
    IUniswapV3Pool public override pool;
    // Accrued protocol fees in terms of token0
    uint256 public accruedProtocolFees0;
    // Accrued protocol fees in terms of token1
    uint256 public accruedProtocolFees1;
    // Total lifetime accrued users fees in terms of token0
    uint256 public usersFees0;
    // Total lifetime accrued users fees in terms of token1
    uint256 public usersFees1;
    // intermediate variable for user fee token0 calculation
    uint256 public token0PerShareStored;
    // intermediate variable for user fee token1 calculation
    uint256 public token1PerShareStored;
    
    // Address of the Sorbetto's owner
    address public governance;
    // Pending to claim ownership address
    address public pendingGovernance;
    //Sorbetto fragola settings address
    address public strategy;
    // Current tick lower of sorbetto pool position
    int24 public override tickLower;
    // Current tick higher of sorbetto pool position
    int24 public override tickUpper;
    // Checks if sorbetto is initialized
    bool public finalized;
    
    /**
     * @dev After deploying, strategy can be set via `setStrategy()`
     * @param _pool Underlying Uniswap V3 pool with fee = 3000
     * @param _strategy Underlying Sorbetto Strategy for Sorbetto settings
     */
     constructor(
        address _pool,
        address _strategy
    ) ERC20("Popsicle LP V3 EURT/WETH", "PLP") ERC20Permit("Popsicle LP V3 EURT/WETH") {
        pool = IUniswapV3Pool(_pool);
        strategy = _strategy;
        token0 = pool.token0();
        token1 = pool.token1();
        tickSpacing = pool.tickSpacing();
        governance = msg.sender;
    }
    //initialize strategy
    function init() external onlyGovernance {
        require(!finalized, "F");
        finalized = true;
        int24 baseThreshold = tickSpacing * ISorbettoStrategy(strategy).tickRangeMultiplier();
        ( , int24 currentTick, , , , , ) = pool.slot0();
        int24 tickFloor = PoolVariables.floor(currentTick, tickSpacing);
        
        tickLower = tickFloor - baseThreshold;
        tickUpper = tickFloor + baseThreshold;
        PoolVariables.checkRange(tickLower, tickUpper); //check ticks also for overflow/underflow
    }
    
    /// @inheritdoc ISorbettoFragola
     function deposit(
        uint256 amount0Desired,
        uint256 amount1Desired
    )
        external
        payable
        override
        nonReentrant
        checkDeviation
        updateVault(msg.sender)
        returns (
            uint256 shares,
            uint256 amount0,
            uint256 amount1
        )
    {
        require(amount0Desired > 0 && amount1Desired > 0, "ANV");
        uint128 liquidityLast = pool.positionLiquidity(tickLower, tickUpper);
        // compute the liquidity amount
        uint128 liquidity = pool.liquidityForAmounts(amount0Desired, amount1Desired, tickLower, tickUpper);
        
        (amount0, amount1) = pool.mint(
            address(this),
            tickLower,
            tickUpper,
            liquidity,
            abi.encode(MintCallbackData({payer: msg.sender})));

        shares = _calcShare(liquidity, liquidityLast);

        _mint(msg.sender, shares);
        refundETH();
        emit Deposit(msg.sender, shares, amount0, amount1);
    }
    
    /// @inheritdoc ISorbettoFragola
    function withdraw(
        uint256 shares
    ) 
        external
        override
        nonReentrant
        checkDeviation
        updateVault(msg.sender)
        returns (
            uint256 amount0,
            uint256 amount1
        )
    {
        require(shares > 0, "S");


        (amount0, amount1) = pool.burnLiquidityShare(tickLower, tickUpper, totalSupply(), shares,  msg.sender);
        
        // Burn shares
        _burn(msg.sender, shares);
        emit Withdraw(msg.sender, shares, amount0, amount1);
    }
    
    /// @inheritdoc ISorbettoFragola
    function rerange() external override nonReentrant checkDeviation updateVault(address(0)) {

        //Burn all liquidity from pool to rerange for Sorbetto's balances.
        pool.burnAllLiquidity(tickLower, tickUpper);
        

        // Emit snapshot to record balances
        uint256 balance0 = _balance0();
        uint256 balance1 = _balance1();
        emit Snapshot(balance0, balance1);

        int24 baseThreshold = tickSpacing * ISorbettoStrategy(strategy).tickRangeMultiplier();

        //Get exact ticks depending on Sorbetto's balances
        (tickLower, tickUpper) = pool.getPositionTicks(balance0, balance1, baseThreshold, tickSpacing);

        //Get Liquidity for Sorbetto's balances
        uint128 liquidity = pool.liquidityForAmounts(balance0, balance1, tickLower, tickUpper);
        
        // Add liquidity to the pool
        (uint256 amount0, uint256 amount1) = pool.mint(
            address(this),
            tickLower,
            tickUpper,
            liquidity,
            abi.encode(MintCallbackData({payer: address(this)})));
        
        emit Rerange(tickLower, tickUpper, amount0, amount1);
    }

    /// @inheritdoc ISorbettoFragola
    function rebalance() external override onlyGovernance nonReentrant checkDeviation updateVault(address(0))  {

        //Burn all liquidity from pool to rerange for Sorbetto's balances.
        pool.burnAllLiquidity(tickLower, tickUpper);
        
        //Calc base ticks
        (uint160 sqrtPriceX96, int24 currentTick, , , , , ) = pool.slot0();
        PoolVariables.Info memory cache = 
            PoolVariables.Info(0, 0, 0, 0, 0, 0, 0);
        int24 baseThreshold = tickSpacing * ISorbettoStrategy(strategy).tickRangeMultiplier();
        (cache.tickLower, cache.tickUpper) = PoolVariables.baseTicks(currentTick, baseThreshold, tickSpacing);
        
        cache.amount0Desired = _balance0();
        cache.amount1Desired = _balance1();
        emit Snapshot(cache.amount0Desired, cache.amount1Desired);
        // Calc liquidity for base ticks
        cache.liquidity = pool.liquidityForAmounts(cache.amount0Desired, cache.amount1Desired, cache.tickLower, cache.tickUpper);

        // Get exact amounts for base ticks
        (cache.amount0, cache.amount1) = pool.amountsForLiquidity(cache.liquidity, cache.tickLower, cache.tickUpper);

        // Get imbalanced token
        bool zeroForOne = PoolVariables.amountsDirection(cache.amount0Desired, cache.amount1Desired, cache.amount0, cache.amount1);
        // Calculate the amount of imbalanced token that should be swapped. Calculations strive to achieve one to one ratio
        int256 amountSpecified = 
            zeroForOne
                ? int256(cache.amount0Desired.sub(cache.amount0).unsafeDiv(2))
                : int256(cache.amount1Desired.sub(cache.amount1).unsafeDiv(2)); // always positive. "overflow" safe convertion cuz we are dividing by 2

        // Calculate Price limit depending on price impact
        uint160 exactSqrtPriceImpact = sqrtPriceX96.mul160(ISorbettoStrategy(strategy).priceImpactPercentage() / 2) / GLOBAL_DIVISIONER;
        uint160 sqrtPriceLimitX96 = zeroForOne ?  sqrtPriceX96.sub160(exactSqrtPriceImpact) : sqrtPriceX96.add160(exactSqrtPriceImpact);

        //Swap imbalanced token as long as we haven't used the entire amountSpecified and haven't reached the price limit
        pool.swap(
            address(this),
            zeroForOne,
            amountSpecified,
            sqrtPriceLimitX96,
            abi.encode(SwapCallbackData({zeroForOne: zeroForOne}))
        );


        (sqrtPriceX96, currentTick, , , , , ) = pool.slot0();

        // Emit snapshot to record balances
        cache.amount0Desired = _balance0();
        cache.amount1Desired = _balance1();
        emit Snapshot(cache.amount0Desired, cache.amount1Desired);
        //Get exact ticks depending on Sorbetto's new balances
        (tickLower, tickUpper) = pool.getPositionTicks(cache.amount0Desired, cache.amount1Desired, baseThreshold, tickSpacing);

        cache.liquidity = pool.liquidityForAmounts(cache.amount0Desired, cache.amount1Desired, tickLower, tickUpper);

        // Add liquidity to the pool
        (cache.amount0, cache.amount1) = pool.mint(
            address(this),
            tickLower,
            tickUpper,
            cache.liquidity,
            abi.encode(MintCallbackData({payer: address(this)})));
        emit Rerange(tickLower, tickUpper, cache.amount0, cache.amount1);
    }

    // Calcs user share depending on deposited amounts
    function _calcShare(uint128 liquidity, uint128 liquidityLast)
        internal
        view
        returns (
            uint256 shares
        )
    {
        shares = totalSupply() == 0 ? uint256(liquidity) : uint256(liquidity).mul(totalSupply()).unsafeDiv(uint256(liquidityLast));
    }
    
    /// @dev Amount of token0 held as unused balance.
    function _balance0() internal view returns (uint256) {
        return IERC20(token0).balanceOf(address(this));
    }

    /// @dev Amount of token1 held as unused balance.
    function _balance1() internal view returns (uint256) {
        return IERC20(token1).balanceOf(address(this));
    }
    
    /// @dev collects fees from the pool
    function _earnFees() internal returns (uint256 userCollect0, uint256 userCollect1) {
         // Do zero-burns to poke the Uniswap pools so earned fees are updated
        pool.burn(tickLower, tickUpper, 0);
        
        (uint256 collect0, uint256 collect1) =
            pool.collect(
                address(this),
                tickLower,
                tickUpper,
                type(uint128).max,
                type(uint128).max
            );

        // Calculate protocol's and users share of fees
        uint256 feeToProtocol0 = collect0.mul(ISorbettoStrategy(strategy).protocolFee()).unsafeDiv(GLOBAL_DIVISIONER);
        uint256 feeToProtocol1 = collect1.mul(ISorbettoStrategy(strategy).protocolFee()).unsafeDiv(GLOBAL_DIVISIONER);
        accruedProtocolFees0 = accruedProtocolFees0.add(feeToProtocol0);
        accruedProtocolFees1 = accruedProtocolFees1.add(feeToProtocol1);
        userCollect0 = collect0.sub(feeToProtocol0);
        userCollect1 = collect1.sub(feeToProtocol1);
        usersFees0 = usersFees0.add(userCollect0);
        usersFees1 = usersFees1.add(userCollect1);
        emit CollectFees(collect0, collect1, usersFees0, usersFees1);
    }

    /// @notice Returns current Sorbetto's position in pool
    function position() external view returns (uint128 liquidity, uint256 feeGrowthInside0LastX128, uint256 feeGrowthInside1LastX128, uint128 tokensOwed0, uint128 tokensOwed1) {
        bytes32 positionKey = PositionKey.compute(address(this), tickLower, tickUpper);
        (liquidity, feeGrowthInside0LastX128, feeGrowthInside1LastX128, tokensOwed0, tokensOwed1) = pool.positions(positionKey);
    }
    
    /// @notice Pull in tokens from sender. Called to `msg.sender` after minting liquidity to a position from IUniswapV3Pool#mint.
    /// @dev In the implementation you must pay to the pool for the minted liquidity.
    /// @param amount0 The amount of token0 due to the pool for the minted liquidity
    /// @param amount1 The amount of token1 due to the pool for the minted liquidity
    /// @param data Any data passed through by the caller via the IUniswapV3PoolActions#mint call
    function uniswapV3MintCallback(
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external {
        require(msg.sender == address(pool), "FP");
        MintCallbackData memory decoded = abi.decode(data, (MintCallbackData));
        if (amount0 > 0) pay(token0, decoded.payer, msg.sender, amount0);
        if (amount1 > 0) pay(token1, decoded.payer, msg.sender, amount1);
    }

    /// @notice Called to `msg.sender` after minting swaping from IUniswapV3Pool#swap.
    /// @dev In the implementation you must pay to the pool for swap.
    /// @param amount0 The amount of token0 due to the pool for the swap
    /// @param amount1 The amount of token1 due to the pool for the swap
    /// @param _data Any data passed through by the caller via the IUniswapV3PoolActions#swap call
    function uniswapV3SwapCallback(
        int256 amount0,
        int256 amount1,
        bytes calldata _data
    ) external {
        require(msg.sender == address(pool), "FP");
        require(amount0 > 0 || amount1 > 0); // swaps entirely within 0-liquidity regions are not supported
        SwapCallbackData memory data = abi.decode(_data, (SwapCallbackData));
        bool zeroForOne = data.zeroForOne;

        if (zeroForOne) pay(token0, address(this), msg.sender, uint256(amount0)); 
        else pay(token1, address(this), msg.sender, uint256(amount1));
    }

    /// @param token The token to pay
    /// @param payer The entity that must pay
    /// @param recipient The entity that will receive payment
    /// @param value The amount to pay
    function pay(
        address token,
        address payer,
        address recipient,
        uint256 value
    ) internal {
        if (token == weth && address(this).balance >= value) {
            // pay with WETH9
            IWETH9(weth).deposit{value: value}(); // wrap only what is needed to pay
            IWETH9(weth).transfer(recipient, value);
        } else if (payer == address(this)) {
            // pay with tokens already in the contract (for the exact input multihop case)
            TransferHelper.safeTransfer(token, recipient, value);
        } else {
            // pull payment
            TransferHelper.safeTransferFrom(token, payer, recipient, value);
        }
    }
    
    
    /**
     * @notice Used to withdraw accumulated protocol fees.
     */
    function collectProtocolFees(
        uint256 amount0,
        uint256 amount1
    ) external nonReentrant onlyGovernance updateVault(address(0)) {
        require(accruedProtocolFees0 >= amount0, "A0F");
        require(accruedProtocolFees1 >= amount1, "A1F");
        
        uint256 balance0 = _balance0();
        uint256 balance1 = _balance1();
        
        if (balance0 >= amount0 && balance1 >= amount1)
        {
            if (amount0 > 0) pay(token0, address(this), msg.sender, amount0);
            if (amount1 > 0) pay(token1, address(this), msg.sender, amount1);
        }
        else
        {
            uint128 liquidity = pool.liquidityForAmounts(amount0, amount1, tickLower, tickUpper);
            pool.burnExactLiquidity(tickLower, tickUpper, liquidity, msg.sender);
        
        }
        
        accruedProtocolFees0 = accruedProtocolFees0.sub(amount0);
        accruedProtocolFees1 = accruedProtocolFees1.sub(amount1);
        emit RewardPaid(msg.sender, amount0, amount1);
    }
    
    /**
     * @notice Used to withdraw accumulated user's fees.
     */
    function collectFees(uint256 amount0, uint256 amount1) external nonReentrant updateVault(msg.sender) {
        UserInfo storage user = userInfo[msg.sender];

        require(user.token0Rewards >= amount0, "A0R");
        require(user.token1Rewards >= amount1, "A1R");

        uint256 balance0 = _balance0();
        uint256 balance1 = _balance1();

        if (balance0 >= amount0 && balance1 >= amount1) {

            if (amount0 > 0) pay(token0, address(this), msg.sender, amount0);
            if (amount1 > 0) pay(token1, address(this), msg.sender, amount1);
        }
        else {
            
            uint128 liquidity = pool.liquidityForAmounts(amount0, amount1, tickLower, tickUpper);
            (amount0, amount1) = pool.burnExactLiquidity(tickLower, tickUpper, liquidity, msg.sender);
        }
        user.token0Rewards = user.token0Rewards.sub(amount0);
        user.token1Rewards = user.token1Rewards.sub(amount1);
        emit RewardPaid(msg.sender, amount0, amount1);
    }
    
    // Function modifier that calls update fees reward function
    modifier updateVault(address account) {
        _updateFeesReward(account);
        _;
    }

    // Function modifier that checks if price has not moved a lot recently.
    // This mitigates price manipulation during rebalance and also prevents placing orders
    // when it's too volatile.
    modifier checkDeviation() {
        pool.checkDeviation(ISorbettoStrategy(strategy).maxTwapDeviation(), ISorbettoStrategy(strategy).twapDuration());
        _;
    }
    
    // Updates user's fees reward
    function _updateFeesReward(address account) internal {
        uint liquidity = pool.positionLiquidity(tickLower, tickUpper);
        if (liquidity == 0) return; // we can't poke when liquidity is zero
        (uint256 collect0, uint256 collect1) = _earnFees();
        
        
        token0PerShareStored = _tokenPerShare(collect0, token0PerShareStored);
        token1PerShareStored = _tokenPerShare(collect1, token1PerShareStored);

        if (account != address(0)) {
            UserInfo storage user = userInfo[msg.sender];
            user.token0Rewards = _fee0Earned(account, token0PerShareStored);
            user.token0PerSharePaid = token0PerShareStored;
            
            user.token1Rewards = _fee1Earned(account, token1PerShareStored);
            user.token1PerSharePaid = token1PerShareStored;
        }
    }
    
    // Calculates how much token0 is entitled for a particular user
    function _fee0Earned(address account, uint256 fee0PerShare_) internal view returns (uint256) {
        UserInfo memory user = userInfo[account];
        return
            balanceOf(account)
            .mul(fee0PerShare_.sub(user.token0PerSharePaid))
            .unsafeDiv(1e18)
            .add(user.token0Rewards);
    }
    
    // Calculates how much token1 is entitled for a particular user
    function _fee1Earned(address account, uint256 fee1PerShare_) internal view returns (uint256) {
        UserInfo memory user = userInfo[account];
        return
            balanceOf(account)
            .mul(fee1PerShare_.sub(user.token1PerSharePaid))
            .unsafeDiv(1e18)
            .add(user.token1Rewards);
    }
    
    // Calculates how much token is provided per LP token 
    function _tokenPerShare(uint256 collected, uint256 tokenPerShareStored) internal view returns (uint256) {
        uint _totalSupply = totalSupply();
        if (_totalSupply > 0) {
            return tokenPerShareStored
            .add(
                collected
                .mul(1e18)
                .unsafeDiv(_totalSupply)
            );
        }
        return tokenPerShareStored;
    }
    
    /// @notice Refunds any ETH balance held by this contract to the `msg.sender`
    /// @dev Useful for bundling with mint or increase liquidity that uses ether, or exact output swaps
    /// that use ether for the input amount
    function refundETH() internal {
        if (address(this).balance > 0) TransferHelper.safeTransferETH(msg.sender, address(this).balance);
    }

    /**
     * @notice `setGovernance()` should be called by the existing governance
     * address prior to calling this function.
     */
    function setGovernance(address _governance) external onlyGovernance {
        pendingGovernance = _governance;
    }

    /**
     * @notice Governance address is not updated until the new governance
     * address has called `acceptGovernance()` to accept this responsibility.
     */
    function acceptGovernance() external {
        require(msg.sender == pendingGovernance, "PG");
        emit TransferGovernance(governance, pendingGovernance);
        pendingGovernance = address(0);
        governance = msg.sender;
    }

    // Sets new strategy contract address for new settings
    function setStrategy(address _strategy) external onlyGovernance {
        require(_strategy != address(0), "NA");
        strategy = _strategy;
    }
}